Analysis of <Emphasis Type="Italic">p</Emphasis><Superscript>10</Superscript>B scattering within Glauber theory

The differential cross sections for p ¹⁰B scattering are calculated at the energies of 197, 600, and 1000 MeV within Glauber theory. The contributions of single and double collisions are taken into account in the multiple-scattering operator. The contributions of proton collisions with nucleons belonging to various (1s, 1p) shells are estimated in the single-scattering cross sections. A comparison with experimental data and with the result of calculations in the distorted-wave Born approximation (DWBA) at 197 MeV showed that the differential cross sections for p ¹⁰B scattering are adequately described in the region forward scattering angles.     

Effect of the shell structure of nuclei on p 15C and p 15N scattering within diffraction theory

The differential cross sections for elastic proton scattering on ¹⁵C and ¹⁵N nuclei at energies of 150 and 800 MeV were calculated within the diffraction theory of Glauber multiple scattering. Shellmodel wave functions were used in these calculations, and particular attention was given to analyzing the sensitivity of the calculated features to distinctions between the shell structure of the ¹⁵C nucleus and the shell structure of the ¹⁵N nucleus. The calculations were performed in the approximation of double scattering. The multiple-scattering operator was written in a form that permits taking into account collisions with nucleons belonging to different shells. It is shown that the difference in structure between the two nuclei in question leads to substantial distinctions between the differential cross sections for scattering at an energy of 800 MeV and scattering angles larger than 25°.     

Mechanism of elastic and inelastic proton scattering on a 15C nucleus in diffraction theory

The amplitudes for elastic and inelastic proton scattering on the neutron-rich nucleus ¹⁵C (to its J ^?? = 5/2⁺ level in the latter case) in inverse kinematics were calculated within Glauber diffraction theory. First- and second-order terms were taken into account in the multiple-scattering operator. The ¹⁵C wave function in the multiparticle shell model was used. This made it possible to calculate not only respective differential cross sections but also the contribution of proton scattering on nucleons occurring in different shells. The differential cross sections for elastic and inelastic scattering were calculated at the energies of 0.2, 0.6, and 1 GeV per nucleon.     

Elastic Deuteron Scattering on the <Superscript>12</Superscript>C Nucleus within a Three-Body Model

The formalism developed earlier for elastic pd scattering on the basis of Glauber theory with allowance for a total spin dependence is modified by replacing pN amplitudes by amplitudes for N¹²C scattering and is applied to elastic deuteron scattering on the ¹²C nucleus. The amplitudes for elastic N¹²C scattering are obtained within the optical model. Respective numerical calculations performed at the kinetic deuteron-beam energy of 270 MeV lead to results that agree well with data on the differential cross section for d¹²C scattering into the forward hemisphere, but the calculated spin observable A _y ^d agrees with experimental data only qualitatively.     

Scattering of protons by <Superscript>9</Superscript>B and <Superscript>10</Superscript>B isotopes at intermediate energies in the diffraction theory

Differential cross sections of the elastic scattering of protons of intermediate energies by ⁹B and ¹⁰B nuclei are calculated within the Glauber theory. The matrix elements of elastic scattering are derived with a wave function in the three-particle 2αp-model (for ⁹B) and with an oscillatory wave function (for ¹⁰B). The differential cross-sections are calculated with allowance for the triple collisions on ⁹B nuclei and in the approximation of double collisions on ¹⁰B nuclei. The sensitivity of the differential cross-section to the ⁹B nucleus structure is analyzed. The differential cross section of ¹⁰B at E = 197 MeV is compared to the results from calculations using the distorted wave method.     

Effect of the structure of neutron-rich <Superscript>8</Superscript>Li and <Superscript>9</Superscript>Li isotopes on the characteristics of proton elastic scattering

The differential cross sections of proton elastic scattering from ⁸Li and ⁹Li nuclei in inverse kinematics have been calculated. The cross sections were determined within the Glauber diffraction theory with the wave functions of nuclei in the three-particle α-t-n, α-t-2n, and ⁷Li-n-n models. Comparison with the existing experimental data for E = 700 and 60 MeV/nucleon made it possible to draw a conclusion about the quality of the wave functions and the adequacy of the potentials used for their calculations.     

Proton scattering on a 15N nucleus in diffraction theory

Within the Glauber diffraction theory, the differential scattering cross section of protons on the ¹⁵N nucleus was calculated at energies of 0.6 and 1.0 GeV. The ¹⁵N wave function in the shell model was used. The dependence of the differential cross section on the nucleus structure and the contribution of single and double collisions in the multiple scattering operator was taken into account.     

Calculation analyzing power in the elastic scattering of protons on <Superscript>15</Superscript>C and <Superscript>15</Superscript>N nuclei in the diffraction theory

Shell-model wave functions are used to calculate the vector analyzing power in the elastic scattering of 0.2, 0.6, and 1 GeV protons on ¹⁵C and ¹⁵N nuclei within the Glauber diffraction theory. Single and double collisions are allowed for upon the decomposition of multiple scattering. It is shown that the number of oscillations and the amplitude of the analyzing power increase with rising energy in the same angular range.     

Perturbative role in the inelastic electron scattering from <Superscript>29</Superscript>Si

Inelastic electron scattering form factors away from the closed sd -shell are investigated. This investigation covers the low-lying states in ²⁹Si , which is considered according to the many-particle configuration mixing shell model as the ¹⁶O core, plus thirteen nucleons distributed over the entire sd -shell orbits. The investigation concentrates on the perturbative role of the core, which is called core polarization effects, on the inelastic electron scattering form factors. Core polarization effects are taken into consideration through the excitation of nucleons from 1s and 1p core orbits, and also from the 2s -1d valence orbits into higher shells, with 2ℏω excitations. Core polarization matrix elements are calculated with the M3Y effective interaction. For the sd -shell model space, a new Hamiltonian, based on a renormalized G -matrix, USDB, is used. All calculations are performed without adjusting any parameters.     

Structure of neutron-rich Isotopes <Superscript>8</Superscript>Li and <Superscript>9</Superscript>Li and allowance for it in elastic scattering

The differential cross sections for elastic proton scattering on the unstable neutron-rich nuclei ⁸Li and ⁹Li at E = 700 and 60 MeV per nucleon were considered. The ⁸Li nucleus was treated on the basis of the three-body α-t-n model, while the ⁹Li nucleus was considered within the α-t-n and ⁷Li-n-n models. The cross sections in question were calculated within Glauber diffraction theory. A comparison of the results with available experimental data made it possible to draw conclusions on the quality of the wave functions and potential used in the calculations.     

Semiclassical description of the <Superscript>6</Superscript>He+<Superscript>12</Superscript>C elastic scattering

The results of the elastic scattering of ⁶He+¹²C systemat E _Lab = 18 MeV by using the barrier and internal wave decomposition of the S-matrix element within the framework of the WKB method are presented. This is the first detailed study for the interaction of the exotic ⁶He nucleus on different stable nuclei by using a semiclassicalmethod. In this paper, we show that in order to obtain the elastic scattering cross section of the ⁶He+¹²C systemat energies close to the Coulomb barrier, it is vitally important to take into account the inner complex turning points in the calculations and the tunneling effects play a crucial role to explain the experimental data. The semiclassical results are compared with the experimental data as well as the quantum-mechanical one.     

Structure of light neutron-rich nuclei and mechanism of elastic proton scattering

Differential cross sections for elastic p ⁶He, p ⁸Li, and p ⁹Li scattering at two energies of 70 and 700 MeV per nucleon were calculated within the Glauber theory of multiple diffractive scattering. Threeparticle wave functions (α-n-n for ⁶He, α-t-n for ⁸Li, and ⁷Li-n-n for ⁹Li) were used for realistic potentials of intercluster interactions. The sensitivity of elastic scattering to proton-nucleus interaction and to the structure of nuclei was explored. In particular, the dependence of the differential cross section on the contribution of higher order collisions, on scattering on the core and peripheral nucleons, and on the contribution of small wave-function components and their asymptotic behavior was determined. A comparison with available experimental data and with the results of calculations within different formalisms was performed.     

The knockout reaction of <Superscript>15</Superscript>C on a <Superscript>9</Superscript>Be target at intermediate energies

In this work, neutron knockout reactions of ¹⁵C on a ⁹Be target at energy 103 and 250 MeV/nucleon are studied. Using the Eikonal approximation of the Glauber model, total neutron removal cross sections, the stripping and diffractive cross sections as well as ¹⁴C longitudinal momentum distributions are determined in both ¹⁵C ground state and exited states of the wave function. We compared the results of our calculations with the available experimental data obtained recently. The calculated cross sections of ¹⁵C and ¹⁴C reactions, as well as the momentum distribution are in relatively good agreement with available data.     

Microscopic <Emphasis Type="Italic">K</Emphasis><Superscript>+</Superscript>-nucleus optical potential and calculations of differential elastic-scattering cross sections and total reaction cross sections

The differential elastic-scattering cross sections and the total reaction cross sections for the interaction of K ⁺ mesons with ¹²C and ⁴⁰Ca nuclei at beam momenta of 0.635, 0.715, and 0.8 GeV/c are calculated. The microscopic optical potential derived in the high-energy approximation is used in these calculations. It is determined by the amplitude for kaon-nucleon scattering and the density distribution of pointlike nucleons of the target nucleus. In the high-energy approximation, the Klein-Gordon-Fock equation reduces to the form of the Schrödinger equation. It is shown that small distinctions between the reduction methods do not lead to significant changes in differential elastic-scattering cross sections, but the effects of relativization as such are quite large. Good agreement with experimental data on elastic K ⁺ A scattering is attained. The total reaction cross sections can be described upon adding, to the volume potential, a term that takes the form of its derivative and which has a maximum at the periphery, its contribution being fitted to experimental data.     

Peculiarities in total cross sections of reactions with weakly bound nuclei <Superscript>6</Superscript>He, <Superscript>9</Superscript>Li

The energy dependence of the total cross sections for the ⁶He + Si and ⁹Li + Si reactions was measured at beam energies between 5 and 20 MeV per nucleon. The results agree with experimental data published for the ⁶He + Si reaction. New data are obtained for the ⁹Li + Si reaction in the vicinity of a local enhancement of the total cross section. A theoretical analysis of the possible reasons behind the appearance of this peculiarity in the case of collisions of ⁶He and ⁹Li nuclei with silicon target nuclei is performed. In particular, the enhancement may owe its origin to the effect of loosely bound projectile nucleons.     

Rescattering effects during proton scattering on the 15N nucleus

The differential cross section of protons at the ¹⁵N nucleus is calculated in the context of the diffraction Glauber theory for E = 0.2, 0.6, and 1.0 GeV, allowing for the highest multiplicity of collisions (prescatterings). It is shown that the amplitude of the p¹⁵N process can be calculated analytically in the approximation of triple scattering using the envelope wave function of ¹⁵N. Rescattering effects manifest themselves over the entire range of angles, but their role increases at large scattering angles and with an increase in the energy of incident particles.     

Cross section of the <Superscript>3</Superscript>H(d, <Superscript>3</Superscript>He)nn reaction at a deuteron beam energy of 37 MeV

Inclusive spectra and differential cross sections of the ³H(d, ³He)nn reaction, measured at E _d = 36.9 MeV are presented. The shape of ³He spectra was reconstructed by modeling amplitudes of the neutron-neutron final state interaction (Watson-Migdal amplitudes), sequential decay via the ⁴He* resonance (E* = 21.2 MeV, Γ = 0.7 MeV), and their interferences. The model allowed the determination of the angular dependence of the differential cross section of the ³H(d, ³He)nn reaction accompanied by singlet nn-pair production. The results are compared to the supermultiplet potential model of the lightest nuclei interaction.     

Investigating the <Superscript>16</Superscript>O + <Superscript>12</Superscript>C reaction over a wide range of energies

The main aim of this work was to describe the reactions of elastic scattering of ¹⁶O + ¹²C over a wide range of energies in an optical model with an l-dependent core. We obtained a value for the compressibility coefficient that agreed with the one found from data on the giant monopole resonance. We considered the elastic transfer of an α particle to reproduce the cross section in the reverse hemisphere.     

Scattering of pions by <Superscript>9</Superscript>Ве nuclei in the context of the Glauber diffraction theory

The differential cross section of the elastic scattering of π^±-mesons by the ⁹Ве nucleus at energies of 0.6 and 1.0 GeV are calculated using the Glauber theory of multiple scattering. The wave function of the ⁹Ве nucleus is obtained in the three-cluster 2α-n model. The sensitivity of the differential cross sections to the wave functions of a target nucleus, calculated with different intercluster interaction potentials, and to the contribution from different orders of scattering in Glauber operator Ω is studied.     

Role of the nuclear and electromagnetic interactions in the coherent dissociation of the relativistic <Superscript>7</Superscript>Li nucleus into the <Superscript>3</Superscript>H + <Superscript>4</Superscript>He channel

The differential cross section in the transverse momentum Q and a total cross section of (31 ± 4) mb for the coherent dissociation of a 3-A-Ge V/c ⁷Li nucleus through the ³H + ⁴He channel have been measured on emulsion nuclei. The observed Q dependence of the cross section is explained by the predominant supposition of the nuclear diffraction patterns on light (C, N, O) and heavy (Br, Ag) emulsion nuclei. The contributions to the cross section from nuclear diffraction (Q ≤ 400 Me V/c) and Coulomb (Q ≤ 50 Me V/c) dissociations are calculated to be 40.7 and 4 mb, respectively.